Sparse Exploratory Factor Analysis

Nickolay T. Trendafilov (), Sara Fontanella and Kohei Adachi
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Nickolay T. Trendafilov: Open University
Sara Fontanella: Imperial College London
Kohei Adachi: Osaka University

Psychometrika, 2017, vol. 82, issue 3, No 11, 778-794

Abstract: Abstract Sparse principal component analysis is a very active research area in the last decade. It produces component loadings with many zero entries which facilitates their interpretation and helps avoid redundant variables. The classic factor analysis is another popular dimension reduction technique which shares similar interpretation problems and could greatly benefit from sparse solutions. Unfortunately, there are very few works considering sparse versions of the classic factor analysis. Our goal is to contribute further in this direction. We revisit the most popular procedures for exploratory factor analysis, maximum likelihood and least squares. Sparse factor loadings are obtained for them by, first, adopting a special reparameterization and, second, by introducing additional $$\ell _1$$ ℓ 1 -norm penalties into the standard factor analysis problems. As a result, we propose sparse versions of the major factor analysis procedures. We illustrate the developed algorithms on well-known psychometric problems. Our sparse solutions are critically compared to ones obtained by other existing methods.

Keywords: eigenvalue reparameterization; penalties inducing sparseness; optimization on matrix manifolds (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (9)

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DOI: 10.1007/s11336-017-9575-8

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